Geodesic
A Note on Lawton's Theorem
Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 484-489

Voir la notice de l'article provenant de la source Cambridge University Press

We prove Lawton's conjecture about the upper bound on themeasure of the set on the unit circle on which a complex polynomial with a bounded number of coefficients takes small values. Namely, we prove that Lawton's bound holds for polynomials that are not necessarily monic. We also provide an analogous bound for polynomials in several variables. Finally, we investigate the dependence of the bound on the multiplicity of zeros for polynomials in one variable.
DOI : 10.4153/CMB-2016-066-x
Mots-clés : 11R09, 11R06, polynomial, Mahler measure 
Dobrowolski, Edward. A Note on Lawton's Theorem. Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 484-489. doi: 10.4153/CMB-2016-066-x
@article{10_4153_CMB_2016_066_x,
     author = {Dobrowolski, Edward},
     title = {A {Note} on {Lawton's} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {484--489},
     year = {2017},
     volume = {60},
     number = {3},
     doi = {10.4153/CMB-2016-066-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-066-x/}
}
TY  - JOUR
AU  - Dobrowolski, Edward
TI  - A Note on Lawton's Theorem
JO  - Canadian mathematical bulletin
PY  - 2017
SP  - 484
EP  - 489
VL  - 60
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-066-x/
DO  - 10.4153/CMB-2016-066-x
ID  - 10_4153_CMB_2016_066_x
ER  - 
%0 Journal Article
%A Dobrowolski, Edward
%T A Note on Lawton's Theorem
%J Canadian mathematical bulletin
%D 2017
%P 484-489
%V 60
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-066-x/
%R 10.4153/CMB-2016-066-x
%F 10_4153_CMB_2016_066_x

[1] [1] Dobrowolski, E. and Smyth, C., Mahler measures of polynomials that are sums of a bounded number of monomials. arxiv:1 606.04376 [math.NT] Google Scholar

[2] [2] Everest, G. and Ward, T., Heights of polynomials and entropy in algebraic dynamics. Universitext, Springer-Verlag, London, 1999. http://dx.doi.Org/10.1007/978-1-4471-3898-3 Google Scholar

[3] [3] Hajos, G., Solution of problem 41. Mat. Lapok 4(1953), 40–41. Google Scholar

[4] [4] Issa, Z. and Lalin, M., A generalization of a theorem ofBoyd and Lawton. Canad. Math. Bull. 56(2013), no. 4, 759–768. http://dx.doi.Org/10.41 53/CMB-2O12-010-2 Google Scholar

[5] [5] Lawton, W. M., A problem ofBoyd concerning geometric means of polynomials. J. Number Theory 16(1983), no. 3, 356–362. http://dx.doi.Org/1 0.101 6/0022-314X(83)90063-X Google Scholar

[6] [6] Schmidt, K., Dynamical systems of algebraic origin. Progress in Mathematics, 128, Birkhauser Verlag, Basel, 1995. Google Scholar

Cité par Sources :